Power Models & Proportionality

Content

Other

Modelling (Lesson 10/10)

1 / 10

Discussion

Every object in the solar system is pulled by the gravitational force F of the sun, which is given by

F=d2km,

where k is a constant, m is the mass of the object, and d is the distance between the object and the sun.

At a given distance, how can we model the relationship between F and m.

Solution:

Since d is fixed, the quantity d2k is constant. Writing

F=d2km

shows a linear relationship between F and m of the form

F=(d2k)m+0

with slope d2k and intercept 0.

In other words, for any mass m, the force F is always m multiplied by the same constant d2k.